Bradford held Stockport to a goalless draw in a poor game to prevent the home side leapfrogging them into the play-off places.
Stockport had the only chances of a scrappy first half when neither side managed a shot on target.
Kyle Knoyle, making his full Stockport debut after joining from Doncaster, fired over from their first attack and Kyle Wootton should have done better with a header that flew past the post from a corner.
Bradford struggled to create anything but felt aggrieved not to be awarded a penalty after Alex Gilliead went down from a nudge in the back by Will Collar.
Bradford keeper Harry Lewis, whose late grandad Ken Mulhearn won the fourth tier with Stockport, produced two saves to deny the home side in a better second half.
Lewis shovelled away Collar’s shot and then made an unconventional block with his head to deny Neill Byrne’s close-range attempt from Knoyle’s cross.
Bradford manager Mark Hughes was booked for obstructing a throw-in but he will be pleased with the point.
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